Sure, here's the math formula in display mode:

$$
2. \text{设矩阵 } \boldsymbol{A}=\left[\begin{array}{lll}2 & 1 & 0 \\ 1 & 2 & 0 \\ 0 & 0 & 1\end{array}\right], \text{ 矩阵 } \boldsymbol{B} \text{ 满足 } \boldsymbol{A} \boldsymbol{B} \boldsymbol{A}^{*}=2 \boldsymbol{B A}^{*}+\boldsymbol{E}, \text{ 其中 } \boldsymbol{A}^{*} \text{ 为 } \boldsymbol{A} \text{ 的伴随矩阵, } \boldsymbol{E} \text{ 是单位矩阵,则 } |\boldsymbol{B}|=(\quad) 。\\
A. \frac{1}{10}\\
B. \frac{1}{9}\\
C. \frac{1}{8}\\
D. \frac{1}{7}
$$